Abstract
An analytic solution of the "conventional" multiple-trapping problem is obtained for a small quantity of charge moving through a spatially varying, but time-independent, electric field and an arbitrary distribution of traps. The solution is shown to apply to cases of microscopic hopping as well as free-translation through extended states. The solution for a discrete set of traps, simply characterized by their mean times for capture and release (, respectively) appears in the form of convolutions of modified Bessel functions of order unity, but for a uniform electric field and a continuum of traps satisfying the relation with the uniformly spaced on a logarithmic scale, the solution reduces to a simple algebraic form which is identical to the one obtained by Scher and Montroll for their power-law waiting-time distribution function . A general equivalence between trapping and continuous-time random walk (CTRW) is further established which shows that can always be constructed from capture and release kinetics, and vice versa. The new trapping solution (and its equivalence to CTRW) is illustrated by reinterpreting transit-time data on . A trap density satisfying for is obtained, where is the coefficient of and eV (for all traps) is the activation energy for release. With the plausible assumption that the microscopic mobility and capture processes are similarly activated (if at all), a trap density for the half-decade interval of around 7 × is found to satisfy (/V sec), where and are concentrations of traps and transport states, respectively, and is the prefactor in . Both hopping and extendedstate motion are compatible with these results, but the most plausible tentative view is hopping with and /V sec. Additional photo- and dark-conduction data could significantly reduce the range of plausible values.
- Received 13 January 1977
DOI:https://doi.org/10.1103/PhysRevB.16.2362
©1977 American Physical Society